Quasilinear dirichlet problems in RN with critical growth

In this study, a given quasilinear problem is solved using variational methods. In particular, the existence of nontrivial solutions for GP is examined using minimax methods. The main theorem on the existence of a nontrivial solution for GP is detailed.

Neural network detection of grinding burn from acoustic emission

An artificial neural network (ANN) approach is proposed for the detection of workpiece `burn', the undesirable change in metallurgical properties of the material produced by overly aggressive or otherwise inappropriate grinding. The grinding acoustic emission (AE) signals for 52100 bearing steel were collected and digested to extract feature vectors that appear to be suitable for ANN processing. Two feature vectors are represented: one concerning band power, kurtosis and skew; and the other autoregressive (AR) coefficients. The result (burn or no-burn) of the signals was identified on the basis of hardness and profile tests after grinding. The trained neural network works remarkably well for burn detection. Other signal-processing approaches are also discussed, and among them the constant false-alarm rate (CFAR) power law and the mean-value deviance (MVD) prove useful.

PI Stabilization of a Class of Time Delay Systems

In this paper we use the Hermite-Biehler theorem to establish results for the design of proportional plus integral (PI) controllers for a class of time delay systems. We extend results of the polynomial case to quasipolynomials using the property of interlacing in high frequencies of the class of time delay systems considered. A signature for the quasipolynomials in this class is derived and used in the proposed approach which yields the complete set of the stabilizing PI controllers.

PID stabilization of a class of time delay systems

In this paper we use the Hermite-Biehler theorem to establish results for the design of proportional plus integral plus derivative (PID) controllers concerning a class of time delay systems. Using the property of interlacing at high frequencies of the class of systems considered and linear programming we obtain the set of all stabilizing PID controllers. © 2005 IEEE.

Evaluating residues and integrals through negative dimensional integration method (NDIM)

The standard way of evaluating residues and some real integrals through the residue theorem (Cauchy's theorem) is well-known and widely applied in many branches of Physics. Herein we present an alternative technique based on the negative dimensional integration method (NDIM) originally developed to handle Feynman integrals. The advantage of this new technique is that we need only to apply Gaussian integration and solve systems of linear algebraic equations, with no need to determine the poles themselves or their residues, as well as obtaining a whole class of results for differing orders of poles simultaneously.

Developing new radiotherapy techniques using linac based gamma radiation sources

A major challenge in cancer radiotherapy is to deliver a lethal dose of radiation to the target volume while minimizing damage to the surrounding normal tissue. We have proposed a model on how treatment efficacy might be improved by interfering with biological responses to DNA damage using exogenous electric fields as a strategy to drastically reduce radiation doses in cancer therapy. This approach is demonstrated at this Laboratory through case studies with prokaryotes (bacteria) and eukaryotes (yeast) cells, in which cellkilling rates induced by both gamma radiation and exogenous electric fields were measured. It was found that when cells exposed to gamma radiation are immediately submitted to a weak electric field, cell death increases more than an order of magnitude compared to the effect of radiation alone. This finding suggests, although does not prove, that DNA damage sites are reached and recognized by means of long-range electric DNA-protein interaction, and that exogenous electric fields could destructively interfere with this process. As a consequence, DNA repair is avoided leading to massive cell death. Here we are proposing the use this new technique for the design and construction of novel radiotherapy facilities associated with linac generated gamma beams under controlled conditions of dose and beam intensity.

On the zeros of polynomials: An extension of the Enestrom-Kakeya theorem

This paper presents an extension of the Enestrom-Kakeya theorem concerning the roots of a polynomial that arises from the analysis of the stability of Brown (K, L) methods. The generalization relates to relaxing one of the inequalities on the coefficients of the polynomial. Two results concerning the zeros of polynomials will be proved, one of them providing a partial answer to a conjecture by Meneguette (1994)[6]. (C) 2011 Elsevier B.V. All rights reserved.

Stabilizing a class of time delay systems using the Hermite-Biehler theorem

In this paper we use the Hermite-Biehler theorem to establish results for the design of fixed order controllers for a class of time delay systems. We extend results of the polynomial case to quasipolynomials using the property of interlacing in high frequencies of the class of time delay systems considered. (C) 2003 Elsevier B.V. All rights reserved.

An existence theorem for an analytic first order PDE in the framework of Colombeau's theory

We study the existence of a holomorphic generalized solution u of the PDE[GRAPHICS]where f is a given holomorphic generalized function and (alpha (1),...alpha (m)) is an element of C-m\{0}.

INEQUALITIES FOR ZEROS of JACOBI POLYNOMIALS VIA OBRECHKOFF'S THEOREM

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Finiteness theorem for topological contact equivalence of map germs

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Blumenthal's theorem for Laurent orthogonal polynomials

We investigate polynomials satisfying a three-term recurrence relation of the form B-n(x) = (x - beta(n))beta(n-1)(x) - alpha(n)xB(n-2)(x), with positive recurrence coefficients alpha(n+1),beta(n) (n = 1, 2,...). We show that the zeros are eigenvalues of a structured Hessenberg matrix and give the left and right eigenvectors of this matrix, from which we deduce Laurent orthogonality and the Gaussian quadrature formula. We analyse in more detail the case where alpha(n) --> alpha and beta(n) --> beta and show that the zeros of beta(n) are dense on an interval and that the support of the Laurent orthogonality measure is equal to this interval and a set which is at most denumerable with accumulation points (if any) at the endpoints of the interval. This result is the Laurent version of Blumenthal's theorem for orthogonal polynomials. (C) 2002 Elsevier B.V. (USA).

A homological version of the implicit function theorem

Our objective in this paper is to prove an Implicit Function Theorem for general topological spaces. As a consequence, we show that, under certain conditions, the set of the invertible elements of a topological monoid X is an open topological group in X and we use the classical topological group theory to conclude that this set is a Lie group.

The Noether theorem for geometric actions and area preserving diffeomorphisms on the torus

We find that within the formalism of coadjoint orbits of the infinite dimensional Lie group the Noether procedure leads, for a special class of transformations, to the constant of motion given by the fundamental group one-cocycle S. Use is made of the simplified formula giving the symplectic action in terms of S and the Maurer-Cartan one-form. The area preserving diffeomorphisms on the torus T2=S1⊗S1 constitute an algebra with central extension, given by the Floratos-Iliopoulos cocycle. We apply our general treatment based on the symplectic analysis of coadjoint orbits of Lie groups to write the symplectic action for this model and study its invariance. We find an interesting abelian symmetry structure of this non-linear problem.

Asymmetry of the Aharonov-Bohm diffraction pattern and Ehrenfests theorem

The electron-diffraction pattern for two slits with magnetic flux confined to an inaccessible region between them is calculated. The Aharonov-Bohm effect gives a diffraction pattern that is asymmetric but has a symmetric envelope. In general, both the expected displacement and the kinetic momentum of the electron are nonzero as a consequence of the asymmetry. Nevertheless, Ehrenfests theorems and the conservation of momentum are satisfied. © 1992 The American Physical Society.